Consider a patent race between Firm R and Firm S.

a) Suppose that the patent is worth 25 million dollar. The costs of R&D are 2, 7, and 15 million dollar for moving 1,2, and 3 steps, respectively. Solve the game by backward induction, and draw a location space figure that shows Trigger Zone I and Trigger Zone II, as well as Safety Zone I and II for R and S. Also assign the locations at the southwest corners of the Trigger Zones I and II.